The system would likely be comprised of tandem satellites, one serving as a communications platform, the other carrying an indeterminate number of tungsten rods, each up to 20 feet in length and 1 foot in diameter.

It's an interesting approach. Very heavy objects dropped from a very high altitude carry a lot of potential energy, which is then converted to kinetic energy, which is then used to destroy things.

I wondered though, where does that energy come from? We have to lift those rods into space. How much would it cost?

What is the volume of each rod? The volume of a cylinder is pi * radius2 * length = pi * 0.5ft * 0.5ft * 20ft = 15.7 cubic feet.

What is the weight of each rod? First convert 15.7 cubic feet * (12 in/ft)3 = 27143 cubic inches. Then multiply 27143 cubic inches * 0.7 pounds/cubic inch and we get 19000 pounds.

What is the cost of tungsten? Google pointed me to a Reuters story suggesting prices are quoted in hundreds of dollars per ton. That means the tungsten in this rod should be fairly cheap (under $5000).

What is the cost of lifting something into orbit? This is harder to find; Google pointed at many different costs. The ad I got on that search led me to spacetethers.com, which gives $1000-$2000 per pound. Given that it's the military doing this, I have to take the upper estimate, and say that the cost is $2000/pound * 19000 pounds, giving $38,000,000.

I suppose $38 million could be considered a “reasonable cost” to the military.